Multitype Branching Processes

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Multitype Branching Processes

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Author : Charles J. Mode
language : en
Publisher:
Release Date : 1971

Multitype Branching Processes written by Charles J. Mode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.

Branching Processes

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Author : Krishna B. Athreya
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Branching Processes written by Krishna B. Athreya and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significantly. Many of the classical limit laws are now known in their sharpest form, and there are new proofs that give insight into the results. Our work deals primarily with this decade, and thus has very little overlap with that of Harris. Only enough material is repeated to make the treatment essentially self-contained. For example, certain foundational questions on the construction of processes, to which we have nothing new to add, are not developed. There is a natural classification of branching processes according to their criticality condition, their time parameter, the single or multi-type particle cases, the Markovian or non-Markovian character of the pro cess, etc. We have tried to avoid the rather uneconomical and un enlightening approach of treating these categories independently, and by a series of similar but increasingly complicated techniques. The basic Galton-Watson process is developed in great detail in Chapters I and II.

Branching Processes

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Author : Søren Asmussen
language : en
Publisher:
Release Date : 1983

Branching Processes written by Søren Asmussen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

Branching processes form one of the classical fields of applied probability and are still an active area of research. The field has by now grown so large and diverse that a complete and unified treat ment is hardly possible anymore, let alone in one volume. So, our aim here has been to single out some of the more recent developments and to present them with sufficient background material to obtain a largely self-contained treatment intended to supplement previous mo nographs rather than to overlap them. The body of the text is divided into four parts, each of its own flavor. Part A is a short introduction, stressing examples and applications. In Part B we give a self-contained and up-to-date pre sentation of the classical limit theory of simple branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and i ts continuous time analogue. Part C deals with the limit theory of Il!arkov branching processes with a general set of types under conditions tailored to (multigroup) branching diffusions on bounded domains, a setting which also covers the ordinary multitype case. Whereas the point of view in Parts A and B is quite pedagogical, the aim of Part C is to treat a large subfield to the highest degree of generality and completeness possi"ble. Thus the exposition there is at times quite technical.

Classical And Modern Branching Processes

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Author : Krishna B. Athreya
language : en
Publisher: Springer
Release Date : 1997

Classical And Modern Branching Processes written by Krishna B. Athreya and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

This IMA Volume in Mathematics and its Applications CLASSICAL AND MODERN BRANCHING PROCESSES is based on the proceedings with the same title and was an integral part of the 1993-94 IMA program on "Emerging Applications of Probability." We would like to thank Krishna B. Athreya and Peter J agers for their hard work in organizing this meeting and in editing the proceedings. We also take this opportunity to thank the National Science Foundation, the Army Research Office, and the National Security Agency, whose financial support made this workshop possible. A vner Friedman Robert Gulliver v PREFACE The IMA workshop on Classical and Modern Branching Processes was held during June 13-171994 as part of the IMA year on Emerging Appli cations of Probability. The organizers of the year long program identified branching processes as one of the active areas in which a workshop should be held. Krish na B. Athreya and Peter Jagers were asked to organize this. The topics covered by the workshop could broadly be divided into the following areas: 1. Tree structures and branching processes; 2. Branching random walks; 3. Measure valued branching processes; 4. Branching with dependence; 5. Large deviations in branching processes; 6. Classical branching processes.

Multitype Branching Processes

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Author : Charles Mode
language : en
Publisher:
Release Date : 1971

Multitype Branching Processes written by Charles Mode and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Branching processes categories.

Multitype Branching Processes

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Author : Steven Goldstein
language : en
Publisher:
Release Date : 1988

Multitype Branching Processes written by Steven Goldstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with categories.

Branching Processes

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Author : C.C. Heyde
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Branching Processes written by C.C. Heyde and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume presents the edited proceedings of the First World Congress on Branching Processes. The contributions present new research and surveys of the current research activity in this field. As a result, all those undertaking research in the subject will find this a timely and high-quality volume to have on their shelves.

Multitype Branching Processes In Random Environments

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Author : Edward Wells Weissner
language : en
Publisher:
Release Date : 1970

Multitype Branching Processes In Random Environments written by Edward Wells Weissner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Markov processes categories.

Consider the k-type Galton-Watson process. The work removes the restrictive assumption that particles of the same type always divide in accordance with the same probability generating function (p.g.f.). Instead, it is assumed that at each unit of time, Nature chooses a k-vector of p.g.f.s from a class of k-vectors of p.g.f.s., independently of the population, past and present, and the previously selected k-vectors, which is then assigned to the present population. Each particle of the present population then splits or disintegrates, independently of the others, in accordance with the p.g.f. assigned to its classification. This process is called a multitype branching process in a random environment (MBPRE). The work gives some necessary and some sufficient conditions for almost certain extinction of the MBPRE when there are at least two particle classifications. To obtain these results, Jensen's inequality, the dual process suggested by Smith and Wilkinson, and some results on products of random matrices are used. Since the theorems require the user to evaluate limits of sequences of products of random arrays, some corollaries are included which involve simpler, albeit less general, conditions. (Author).

Branching Processes

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Author : Asmussen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Branching Processes written by Asmussen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.

Branching processes form one of the classical fields of applied probability and are still an active area of research. The field has by now grown so large and diverse that a complete and unified treat ment is hardly possible anymore, let alone in one volume. So, our aim here has been to single out some of the more recent developments and to present them with sufficient background material to obtain a largely self-contained treatment intended to supplement previous mo nographs rather than to overlap them. The body of the text is divided into four parts, each of its own flavor. Part A is a short introduction, stressing examples and applications. In Part B we give a self-contained and up-to-date pre sentation of the classical limit theory of simple branching processes, viz. the Gal ton-Watson ( Bienayme-G-W) process and i ts continuous time analogue. Part C deals with the limit theory of Il!arkov branching processes with a general set of types under conditions tailored to (multigroup) branching diffusions on bounded domains, a setting which also covers the ordinary multitype case. Whereas the point of view in Parts A and B is quite pedagogical, the aim of Part C is to treat a large subfield to the highest degree of generality and completeness possi"ble. Thus the exposition there is at times quite technical.

Limiting Distributions For Critical Multitype Branching Processes

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Author : T. W. Mullikin
language : en
Publisher:
Release Date : 1961

Limiting Distributions For Critical Multitype Branching Processes written by T. W. Mullikin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Branching processes categories.